At still only 23, though, the FC Bayern Munich forward still has a good decade to add to his list of honours. And for all he has achieved already, the thoroughbred Bavarian remains hungrier than ever.
Indeed, defeat in both of those Champions League finals, semi-final exits at each of the last two major international tournaments and two seasons without a domestic trophy have only made Müller all the more determined, something his performances so far this season pay ample testimony to.
The FC Bayern No25 is the Bundesliga's most effective attacking player this term, having scored seven goals and set up a further five. On average, he has been involved in a goal every 65 minutes. With only eleven league matches played, Müller has already matched his goal tally for the whole of last season -a result, it would seem, of improved precision. In the current campaign, the gangly goalgetter has dispatched 80 per cent of the clear-cut chances that have come his way. Last season he 'only' managed eight from twelve.
Strength in depth
So how could Bayern afford to leave out their most dangerous player in Saturday's 2-0 win against Eintracht Frankfurt? Simple. Müller is not the only one enjoying arguably the best season of his career to date.
Coach Jupp Heynckes is in the enviable position of having strength in depth throughout his squad, perhaps nowhere more so than in the central midfield positions, both attacking and defensive. With Arjen Robben and Franck Ribery more or less guaranteed the two wing berths when fit and Bastian Schweinsteiger, Javi Martinez and Luiz Gustavo better suited to the deep-lying roles, Müller is more often than not having to battle it out for a place with another of the country's stand-out talents, Toni Kroos.
License to roam
On Saturday, it was the latter who slotted in behind lone forward Claudio Pizarro, with Müller having to be content with a seat in the dugout. In fine fettle himself, Kroos impressed with a chipped pass to set up Ribery for Bayern's first goal - only his second assist of the season, but the seventh time all-told that the 22-year-old Germany international had carved out a scoring opportunity.
With Müller and Kroos creating chances in abundance in the final third, you might think that Schweinsteiger could concentrate on his defensive duties. However, with the FCB backline conceding just four goals all season, the man the Munich crowd call Fußballgott [football god, ed.] has been venturing forward more than ever.
Schweinsteiger has already netted more goals (four) than he did last season (three) and is well on course to beat his personal-best tally of five from the 2008/09 campaign, no coincidence given that he has made strides into the final third almost as many times he did in the entirety of last term.
Though the latter may be a touch older than Müller and Kroos at 28, what all three have in common is that they were schooled by the prolific Bayern youth academy. Needless to say, the Rekordmeister have been the chief beneficiaries of their own star gardening, but the emergence of home-grown talent has also been one of the chief factors behind the German national team's fortunes in recent years.
Müller, Kroos and Schweinsteiger are well on their way to a double century of caps collectively and all three are in Joachim Löw's squad to face the Netherlands Wednesday's friendly. Unsurprisingly, if Müller has anything to do with it, Bayern's key three will all be starting: "It's a great fixture and one we're all looking forward to. We'll be representing our country with passion and doing what we were born to do: playing football for Germany."
Andy James in Munich